AbstractIn this paper, optimal inventory lot-sizing models are developed for deteriorating items with general continuous time-varying demand over a finite planning horizon and under three replenishment policies. The deterioration rate is assumed to be a constant fraction of the on-hand inventory. Shortages are permitted and are completely backordered. The proposed solution procedures are shown to generate global minimum replenishment schedules for both general increasing and decreasing demand patterns. An extensive empirical comparison using randomly generated linear and exponential demands revealed that the replenishment policy which starts with shortages in every cycle is the least cost policy and the replenishment policy which prohibits shortages in the last cycle exhibited the best service level effectiveness. An optimal procedure for the same problem with trended inventory subject to a single constraint on the minimum service level (maximum fraction of time the inventory system is out of stock during the planning horizon) is also proposed in this paper.